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HM Chan

Publications and source records attributed to HM Chan.

At least 19 recordsLinked to original sources
arXiv2023

A vacuum transition in the FSM with a possible new take on the horizon problem in cosmology

The framed standard model (FSM), constructed to explain the empirical mass and mixing patterns of quarks and leptons, gives the same result as the standard model in almost all areas in particle physics where it has been successfully applied, except for a few deviations such as the W mass and the g-2 of muons, where experiment is showing departures from what SM predicts. It predicts further the existence of a hidden sector of particles which may function as dark matter. In this paper, we first note that the above results involve the FSM undergoing a vacuum transition at a scale of around 17 MeV, where the vev's of the colour framons which are all nonzero above that scale acquire some vanishing components below it. This implies that the metric pertaining to these vanishing components would vanish also. Consequences should then ensue, mostly in the unknown hidden sector where empirical confirmation is hard at present to come by, but they give small reflections in the standard sector, some of which may have already been seen. However, one notes that if one imagines colour to be embedded, Kaluza-Klein fashion, into a higher dimensional space-time, then this VTR1 would cause 2 of the compactified dimensions to collapse. This might mean that when the universe cooled to the corresponding temperature of $10^{11}$K when it was about $10^{-3}$s old, this VTR1 collapse would cause the 3 spatial dimensions of the universe to expand to compensate. The resultant expansion is estimated, using FSM parameters previously determined from particle physics, to be capable, when extrapolated backwards in time, of bringing the present universe back inside the then horizon, solving thus formally the horizon problem. Besides, VTR1 being a global phenomenon in the FSM, it would switch on and off automatically and simultaneously over all space, thus requiring no additional strategy for a graceful exit.

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arXiv2022

Resolving an ambiguity of Higgs couplings in the FSM, greatly improving thereby the model's predictive range and prospects

We show that, after resolving what was thought to be an ambiguity in the Higgs coupling, the FSM gives, apart from two extra terms (i) and (ii) to be specified below, an effective action in the standard sector which has the same form as the SM action, the two differing only in the values of the mass and mixing parameters of quarks and leptons which the SM takes as inputs from experiment while the FSM obtains as a result of a fit with a few parameters. Hence, to the accuracy that these two sets of parameters agree in value, and they do to a good extent as shown in earlier work, the FSM should give the same result as the SM in all the circumstances wherethe latter has been successfully applied, except for the noted modifications due to (i) and (ii). If so, it would be a big step forward for the FSM. The correction terms are: (i) a mixing between the SM's $\gamma - Z$ with a new vector boson in the hidden sector, (ii) a mixing between the standard Higgs with a new scalar boson also in the hidden sector. And these have been shown a few years back to lead to (i$'$) an enhancement of the $W$ mass over the SM value \cite{zmixed}, and (ii$'$) effects consistent with the $g - 2$ and some other anomalies, precisely the two deviations from the SM reported by experiments \cite{Wmassnew,g-2new} recently much in the news.

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arXiv2022

Two variations on the theme of Yang and Mills -- the SM and the FSM

The standard model (SM) is viewed as a variation on the Yang-Mills theory with gauge symmetry $u(1) \times su(2) \times su(3)$, in which the flavour symmetry is framed and to which 3 generations of quarks and leptons are appended as inputs from experiment. The framed standard model (FSM) is then a further variation on the SM in which the colour symmetry is also framed, where the 3 generations now follow as consequences together with their characteristic mass and mixing patterns. In addition, the FSM yields as a bonus a solution to the strong CP problem leading to a unified treatment seemingly of all known CP physics for both quarks and leptons. It predicts, however, also a "hidden" sector populated by particles yet unknown, hence full both of promises (e.g.\ dark matter?) and of threats, which is just beginning to be explored (i) with a modified Weinberg mixing and (ii) with the $g-2$ and some other anomalies.

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arXiv2015

The Framed Standard Model (II) - A first Test against Experiment

Apart from the qualitative features described in \cite{chm}, the renormalization group equation derived for the rotation of the fermion mass matrices are amenable to quantitative study. The equation depends on a coupling and a fudge factor and, on integration, on 3 integration constants. Its application to data analysis, however, requires the input from experiment of the heaviest generation masses $m_t, m_b, m_\tau, m_{\nu_3}$ all of which are known, except for $m_{\nu_3}$. Together then with the theta-angle in the QCD action, there are in all 7 real unknown parameters. Determining these 7 parameters by fitting to the experimental values of the masses $m_c, m_\mu, m_e$, the CKM elements $|V_{us}|, |V_{ub}|$, and the neutrino oscillation angle $\sin^2\theta_{13}$, one can then calculate and compare with experiment the following 12 other quantities $m_s, m_u/m_d, |V_{ud}|, |V_{cs}|, |V_{tb}|, |V_{cd}|, |V_{cb}|, |V_{ts}|, |V_{td}|, J, \sin^2 2\theta_{12}, \sin^2 2\theta_{23}$, and the results all agree reasonably well with data, often to within the stringent experimental error now achieved. Counting the predictions not yet measured by experiment, this means that 17 independent parameters of the standard model are now replaced by 7 in the FSM.

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arXiv2015

The Framed Standard Model (I) - A Physics Case for Framing the Yang-Mills Theory?

Introducing, in the underlying gauge theory of the Standard Model, the frame vectors in internal space as field variables (framons), in addition to the usual gauge boson and matter fermions fields, one obtains: * the standard Higgs scalar as the framon in the electroweak sector; * a global $\widetilde{su}(3)$ symmetry dual to colour to play the role of fermion generations. Renormalization via framon loops changes the orientation in generation space of the vacuum, hence also of the mass matrices of leptons and quarks, thus making them rotate with changing scale $\mu$. From previous work, it is known already that a rotatiing mass matrix will lead automatically to: * CKM mixing and neutrino oscillations, * hierarachical masses for quarks and leptons, * a solution to the strong-CP problem transforming the theta-angle into a Kobayashi-Maskawa phase. Here in the FSM, the renormalization group equation has some special properties which explain the main qualitative feaures seen in experiment both for mixing matrices of quarks and leptons, and for their mass spectrum. Quantitative results will be given in (II). The paper ends with some tentative predictions on Higgs decay, and with some speculations on the origin of dark matter.

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arXiv2014

A First Test of the Framed Standard Model against Experiment

The framed standard model (FSM) is obtained from the standard model by incorporating, as field variables, the frame vectors (vielbeins) in internal symmetry space. It gives the standard Higgs boson and 3 generations of quarks and leptons as immediate consequences. It gives moreover a fermion mass matrix of the form: $m = m_T \alpha \alpha^\dagger$, where $\alpha$ is a vector in generation space independent of the fermion species and rotating with changing scale, which has already been shown to lead, generically, to up-down mixing, neutrino oscillations and mass hierarchy. In this paper, pushing the FSM further, one first derives to 1-loop order the RGE for the rotation of $\alpha$, and then applies it to fit mass and mixing data as a first test of the model. With 7 real adjustable parameters, 18 measured quantities are fitted, most (12) to within experimental error or to better than 0.5 percent, and the rest (6) not far off. (A summary of this fit can be found in Table 2 in the text.) Two notable features, both generic to FSM, not just specific to the fit, are: (i) that a theta-angle of order unity in the instanton term in QCD would translate via rotation into a Kobayashi-Maskawa phase in the CKM matrix of about the observed magnitude ($J \sim 10^{-5}$), (ii) that it would come out correctly that $m_u<m_d$, despite the fact that $m_t \gg m_b, m_c \gg m_s$. Of the 18 quantities fitted, 12 are deemed independent in the usual formulation of the standard model. In fact, the fit gives a total of 17 independent parameters of the standard model, but 5 of these have not been measured by experiment.

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arXiv2003

Updates to the Dualized Standard Model on Fermion Masses and Mixings

The Dualized Standard Model has scored a number of successes in explaining the fermion mass hierarchy and mixing pattern. This note contains updates to those results including (a) an improved treatment of neutrino oscillation free from previous assumptions on neutrino masses, and hence admitting now the preferred LMA solution to solar neutrinos, (b) an understanding of the limitation of the 1-loop calculation so far performed, thus explaining the two previous discrepancies with data, and (c) an analytic derivation and confirmation of the numerical results previously obtained.

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arXiv2002

Circumstantial Evidence for Rotating Mass Matrix from Fermion Mass and Mixing Data

It is shown that existing data on the mixing between up and down fermion states and on the hierarchical mass ratios between fermion generations, as far as can be so analysed at present, are all consistent with the two phenomena being both consequences of a mass matrix rotating in generation space with changing energy scale. As a result, the rotating mass matrix can be traced over some 14 orders of magnitude in energy from the mass scale of the $t$-quark at 175 GeV to below that of the atmospheric neutrino at 0.05 eV.

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arXiv2001

Kinematical Lepton Transmutation in $e^+ e^-$ Collision and Vector Boson Decay

The change in orientation in generation space (rotation) of the fermion mass matrix with changing scales can lead to flavour-violations through just the kinematics of a non-diagonal mass matrix. Such effects for the reactions: $e^+ e^- \longrightarrow e^\pm μ^\mp, e^\pm τ^\mp, μ^\pm τ^\mp$, and for the decays of vector bosons into the same channels, are calculated following a method suggested earlier which gives the differential cross section for each reaction and the branching ratio for each decay mode in terms of an overall normalization depending only on the speed at which the mass matrix rotates. A rotation speed estimated earlier, under certain assumptions from the fermion mixing angles and mass ratios, is found to give the above effects at a level readily detectable in modern high sensitivity experiments such as Bepc, Cleo, BaBar and Belle, at least in principle. The observation of these effects would not only confirm the concept of a rotating mass matrix with a significance on par with the running coupling constant, but also offer some valuable insight into the origin of fermion generations. However, a negative result cannot unfortunately rule out the rotating mass matrix since the effects deduced here from this mechanism alone could in principle be cancelled by other rotation effects.

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arXiv2000

Experimental implications of the dual colour solution to the generation puzzle

Apart from offering explanations not only for the distinctive fermion mass and mixing patterns but also for the actual values of the mass and mixing parameters, the dual colour solution to the generation puzzle gives numerous detailed predictions ranging from rare FCNC meson decays and $μ$-$e$ conversions in nuclei at low energies to cosmic ray air showers with energies beyond $10^{20}$ eV at the extreme end of the experimental range. Besides, it predicts a new class of flavour-violating phenomena (called transmutations) due to the rotating fermion mass matrix which are unambiguously calculable. Comparison with experiment of these many ``parameter-free'' predictions reveals no violation of existing bounds but identifies several striking effects which can be tested with present experimental sensitivity.

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arXiv2000

Yang-Mills Duality and the Generation Puzzle

The fermion generation puzzle has survived into this century as one of the great mysteries in particle physics. We consider here a possible solution within the Standard Model framework based on a nonabelian generalization of electric-magnetic duality. First, by constructing in loop space a nonabelian generalization of the abelian dual transform (Hodge *), one finds that a ``magnetic'' symmetry exists also in classical Yang-Mills theory dual to the original (``electric'') gauge symmetry. Secondly, from a result of 't Hooft's, one obtains that for confined colour SU(3), the dual symmetry $\widetilde{SU}(3)$ is spontaneously broken and can play the role of the ``horizontal symmetry'' for generations. Thirdly, such an identification not only offers an explanation why there should be three and apparently only three generations of fermions with the remarkable mass and mixing patterns seen in experiment, but allows even a calculation of the relevant parameters giving very sensible results. Other testible predictions follow ranging from rare hadron decays to cosmic ray air showers.

hep-th↗
arXiv2000

Photo-Transmutation of Leptons

By photo-transmutation of leptons we mean photon-lepton reactions of the following type: $γl_α\longrightarrow γl_β$ with $l_α\neq l_β$, occurring as a consequence of the lepton mass matrix changing its orientation (rotating) under changing scales. In this paper, we first discuss these reactions in general terms, then proceed to the calculation of their cross sections in two specific schemes, one within the framework of the conventional Standard Model, the other being the so-called Dualized Standard Model we ourselves advocate. Although the cross section obtained is generally small the calculation reveals certain special circumstances where these reactions may be accessible to experiment, for example with virtual photons in LEP for $γe \longrightarrow γτ$, and in BEPC for $γe \longrightarrow γμ$.

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arXiv2000

Implications of a Rotating Mass Matrix

The fermion mass matrix, in addition to having eigenvalues (masses) which run, also changes its orientation (rotates) with changing energy scales. This means that its eigenstates at one scale will no longer be eigenstates at another scale, leading to effects where fermions of different flavours can ``transmute'' into one another. In this paper, the implications of a rotating mass matrix are analysed and possible transmuation effects are investigated both in the Standard Model (SM) and in the so-called Dualized Standard Model (DSM) that we advocate, arriving at the conclusion that some transmutational decays such as $ψ\longrightarrow μτ$, $Υ\longrightarrow μτ$ or $π^0 \longrightarrow e μ$ may be within experimental range, if not immediately, then in the near future.

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arXiv1999

The Dualized Standard Model and its Applications---an Interim Report

Based on a nonabelian generalization of electric-magnetic duality, the Dualized Standard Model (DSM) suggests a natural explanation for exactly 3 generations of fermions as the `dual colour' $\widetilde{SU}(3)$ symmetry broken in a particular manner. The resulting scheme then offers on the one hand a fermion mass hierarchy and a perturbative method for calculating the mass and mixing parameters of the Standard Model fermions, and on the other testable predictions for new phenomena ranging from rare meson decays to ultra-high energy cosmic rays. Calculations to 1-loop order gives, at the cost of adjusting only 3 real parameters, values for the following quantities all (except one) in very good agreement with experiment: the quark CKM matrix elements $|V_{rs}|$, the lepton CKM matrix elements $|U_{rs}|$, and the second generation masses $m_c, m_s, m_μ$. This means, in particular, that it gives near maximal mixing $U_{\mu3}$ between $ν_μ$ and $ν_τ$ as observed by SuperKamiokande, Kamiokande and Soudan, while keeping small the corresponding quark angles $V_{cb}, V_{ts}$. In addition, the scheme gives (i) rough order-of-magnitude estimates for the masses of the lowest generation, (ii) predictions for low energy FCNC effects such as $K_L \to e μ$, (iii) a possible explanation for the long-standing puzzle of air showers beyond the GZK cut-off. All these together, however, still represent but a portion of the possible physical consequences derivable from the DSM scheme the majority of which are yet to be explored.

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